Determinant Formulae of Matrices with Certain Symmetry and Its Applications

Abstract

In this paper, we introduce formulae for the determinants of matrices with certain symmetry. As applications, we will study the Alexander polynomial and the determinant of a periodic link which is presented as the closure of an oriented 4-tangle.

Keywords

• determinant of a matrix
• Seifert matrix of a link
• periodic links
• Alexander polynomial of a link